题目内容
用四个阻值均为R的电阻连成如图所示的电路,开关S闭合时,有一质量为
,带电荷量为
的小球静止于水平放置的平行板电容器的中点,平行板电容器的下极板接地。现打开开关S,这个带电小球便向平行板电容器的一个极板运动,并和此板碰撞,碰撞过程中小球没有机械能损失,只是碰后小球所带电荷量发生变化,碰后小球带有和该极板同种性质的电荷,并恰能运动到另一极板,设两极板间距离为
,不计电源内阻,求:
(1)小球开始带什么电?小球开始在中点的电势是多少?电源电动势E为多大?
(2)小球与极板碰撞后所带的电荷量
为多少?![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241228337063916.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122833659204.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122833659199.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122833675198.gif)
(1)小球开始带什么电?小球开始在中点的电势是多少?电源电动势E为多大?
(2)小球与极板碰撞后所带的电荷量
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122833690210.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241228337063916.jpg)
(1)负
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122833737270.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122833721666.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122833737270.gif)
(1)当S闭合时,小球静止于水平放置的平行板电容器的中点,上极板电势高于下极板,对带电小球进行受力分析,可知小球带负电荷,设电容器电压为U,则有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122833753851.gif)
解得:
则小球开始在中点的电势
……………………6分
(2)设断开S后,电容器的电压为
,则:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122833799601.gif)
因为碰撞过程中小球没有机械能损失,只是碰后小球所带电荷量发生变化,所以对带电小球运动的全过程根据动能定理得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122833815710.gif)
解得:
………………………4分
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122833753851.gif)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122833768765.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122833768631.gif)
(2)设断开S后,电容器的电压为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122833784215.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122833799601.gif)
因为碰撞过程中小球没有机械能损失,只是碰后小球所带电荷量发生变化,所以对带电小球运动的全过程根据动能定理得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122833815710.gif)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824122833831349.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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